no. 3
Monodromies at infinity of non-tame polynomials
[Monodromies à l'infini des polynômes non-modérés]
Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 3, pp. 477-506

Polynomials that we usually encounter in mathematics are non-convenient and hence non-tame at infinity. We consider the monodromy at infinity and the monodromies around the bifurcation points of polynomial functions f:ℂn⟶ℂ which are non-tame at infinity and might have non-isolated singularities. Our description of their Jordan blocks in terms of the Newton polyhedra and the motivic Milnor fibers relies on two new issues: the non-atypical eigenvalues of the monodromies and the corresponding concentration results for their generalized eigenspaces.

Les polynômes qu'on rencontre d'habitude en mathématiques sont généralement non-commodes et donc non-modérés à l'infini. On considère ici la monodromie à l'infini et les monodromies autour les valeurs de bifurcation des fonctions polynômiales f:ℂn⟶ℂ qui sont non-modérés à l'infini et peuvent avoir des singularités non-isolées. Notre description de leurs blocs de Jordan en termes des polyèdres de Newton et des fibres de Milnor motiviques s'appuie sur deux nouveaux concepts : les valeurs propres non-atypiques des monodromies et les résultats de concentration pour leurs espaces propres généralisés.

Publié le :
DOI : 10.24033/bsmf.2720
Classification : 14E18, 14M25, 32C38, 32S35, 32S40
Keywords: Atypical values, non-convenient polynomials, monodromy at infinity, Jordan blocks, motivic Milnor fibre, Newton polyhedron, toric compactification.
Mots-clés : Valeurs atypiques, polynômes non-commodes, monodromie à l'infini, blocs de Jordan, fibre de Milnor motivique, polyèdre de Newton, compactification torique. 
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     title = {Monodromies at infinity of non-tame polynomials},
     journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
     pages = {477--506},
     year = {2016},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {144},
     number = {3},
     doi = {10.24033/bsmf.2720},
     mrnumber = {3558430},
     zbl = {1388.14052},
     language = {en},
     url = {https://www.numdam.org/articles/10.24033/bsmf.2720/}
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Takeuchi, Kiyoshi; Tibăr, Mihai. Monodromies at infinity of non-tame polynomials. Bulletin de la Société Mathématique de France, Tome 144 (2016) no. 3, pp. 477-506. doi: 10.24033/bsmf.2720

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